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The centrally extended su(2|2) superalgebra is an asymptotic symmetry of thelight-cone string sigma model on AdS5 x S5. We consider an evaluationrepresentation of the conventional Yangian built over a particular16-dimensional long representation of the centrally extended su(2|2).Interestingly, we find that S-matrices compatible with this evaluationrepresentation do not exist. On the other hand, by requiring centrally extendedsu(2|2) invariance and explicitly solving the Yang-Baxter equation, we find ascattering matrix for long-short representations of the Lie superalgebra. Wenotice that this S-matrix is invariant under a different representation ofnon-evaluation type, induced from the tensor product of short representations.Our findings concern the conventional Yangian only, and are not applied topossible algebraic extensions of the latter.

On Yangian and Long Representations of the Centrally Extended su(2|2) Superalgebra